How to animate a closed string as in string theory
I think he has used a Displace modifier:


Create a circle, extrude, deform a bit, give it a Displace modifier and a Subdivision Surface modifier. Choose the Displace Direction:





In the Displace modifier, click on Texture > New, and in the Texture tab, go select the Clouds texture. Play with the Size and Depth.





When you'll move the circle it will deform along the given direction.